Question

Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

score 1k · Answer 1 · 2026-03-30 14:42:08

1k

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Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Published on 30 Mar 2026 - 14:42

score 67 · Answer 2 · 2026-04-10 03:10:09

67

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Using induction on modified inequalities.

Published on 10 Apr 2026 - 3:10

score 145 · Answer 3 · 2026-03-28 04:35:44

145

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Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$

Published on 28 Mar 2026 - 4:35

score 331 · Answer 4 · 2026-04-11 17:25:08

331

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How to prove by induction that $4^{2n}-3^{2n}-7$ is divisible by 84 for any n starting from 1?

Published on 11 Apr 2026 - 17:25

score 297 · Answer 5 · 2026-04-12 08:25:59

297

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Polynomial ,divides and Induction Proof?

Published on 12 Apr 2026 - 8:25

score 71 · Answer 6 · 2016-07-08 05:12:49

71

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Show $\sum_{i=1}^{n+1} 2^ii = 2^{n+2}n+2$ , for all integers $n\ge 0$ using induction.

Published on 08 Jul 2016 - 5:12

score 86 · Answer 7 · 2026-04-07 21:21:01

86

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Prove that $ \text{len}(q^*) \le 3\text{len}(q) -2 $

Published on 07 Apr 2026 - 21:21

score 153 · Answer 8 · 2016-07-08 20:27:09

Proving that $1\cdot 2+2\cdot 3+\cdots+n\left( n+1 \right) =\frac { n\left( n+1 \right) \left( n+2 \right) }{ 3 } $ by induction

score 170 · Answer 9 · 2026-04-11 10:46:55

170

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Show that for each positive integer $n$, $a_n$ is a positive integer, $a_{n+1} = (a_n+1)a+(a+1)a_n+2\sqrt{a(a+1)a_n(a_n+1)} \quad (n = 1,2,\ldots).$

Published on 11 Apr 2026 - 10:46

score 595 · Answer 10 · 2026-04-11 13:52:23

595

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Use the PMI to prove the following $4^{k}-1$ is divisible by 3.

Published on 11 Apr 2026 - 13:52

score 51 · Answer 11 · 2026-03-25 20:12:44

51

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How does $af\left(\frac{n}{b}\right) \leq cf(n)$ imply that $a^{i}f\left(\frac{n}{b^{i}}\right) \leq c^{i}f(n)$?

Published on 25 Mar 2026 - 20:12

score 66 · Answer 12 · 2016-07-13 19:34:36

66

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Prove $\sum_{i=1}^{n}\frac{i}{(i+1)!}= 1-\frac1{(n+1)!}$

Published on 13 Jul 2016 - 19:34

score 947 · Answer 13 · 2016-07-15 16:21:42

947

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Proving that $4k < 2^k$ by induction

Published on 15 Jul 2016 - 16:21

score 75 · Answer 14 · 2026-03-29 11:49:58

75

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D. F. Wallace's "Everything and more" $\S$7b : Cantor transfinite derivation from $P^{(n)}$

Published on 29 Mar 2026 - 11:49

score 229 · Answer 15 · 2016-07-17 01:39:26

229

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Proving $a^ma^n=a^{m+n}$ by induction when $n$ or $m$ is negative (or both)

Published on 17 Jul 2016 - 1:39

List Question

Factorial Proof by Induction Question: $ \frac1{2!} + \frac2{3!} + \dots+ \frac{n}{(n+1)!} = 1 - \frac1{(n+1)!} $?

Using induction on modified inequalities.

Prove by induction that $\sum_{i=1}^{2^n} \frac{1}{i} \ge 1+\frac{n}{2}, \forall n \in \mathbb N$

How to prove by induction that $4^{2n}-3^{2n}-7$ is divisible by 84 for any n starting from 1?

Polynomial ,divides and Induction Proof?

Show $\sum_{i=1}^{n+1} 2^ii = 2^{n+2}n+2$ , for all integers $n\ge 0$ using induction.

Prove that $ \text{len}(q^*) \le 3\text{len}(q) -2 $

Proving that $1\cdot 2+2\cdot 3+\cdots+n\left( n+1 \right) =\frac { n\left( n+1 \right) \left( n+2 \right) }{ 3 } $ by induction

Show that for each positive integer $n$, $a_n$ is a positive integer, $a_{n+1} = (a_n+1)a+(a+1)a_n+2\sqrt{a(a+1)a_n(a_n+1)} \quad (n = 1,2,\ldots).$

Use the PMI to prove the following $4^{k}-1$ is divisible by 3.

How does $af\left(\frac{n}{b}\right) \leq cf(n)$ imply that $a^{i}f\left(\frac{n}{b^{i}}\right) \leq c^{i}f(n)$?

Prove $\sum_{i=1}^{n}\frac{i}{(i+1)!}= 1-\frac1{(n+1)!}$

Proving that $4k < 2^k$ by induction

D. F. Wallace's "Everything and more" $\S$7b : Cantor transfinite derivation from $P^{(n)}$

Proving $a^ma^n=a^{m+n}$ by induction when $n$ or $m$ is negative (or both)

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